Finite Group Databasebeta

← D47×#2330 #26375103

Subgroups — D47×#2330 #26375103

Order 12032.

2398 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D47C211yesmaximal, characteristic
2#20246130C211yesmaximal, characteristic, complemented
3#20246129C211yesmaximal, characteristic, complemented
4#20246128C212yesmaximal, complemented
5#20246127C211yesmaximal, characteristic, complemented
6#20246126C214yesmaximal, complemented
7#20246125C212yesmaximal, complemented
8#20246124C214yesmaximal, complemented
9#389×D47C212yesmaximal
10#389×D47C214yesmaximal
11#387×D47C214yesmaximal
12#384×D47C211yesmaximal, characteristic
13C4×C4⋊C4×D47C212yesmaximal
14#376×D47C211yesmaximal, characteristic
15C47×#2330C211yesmaximal, characteristic, complemented
16C2×#13094016C2211yescharacteristic
17C2×#13094015C2212yes—
18C2×#13094014C2214yes—
19#125×D47C4116yescomplemented
20C2×C4⋊C4×D47C2212yes—
21C2×C4⋊C4×D47C2214yes—
22C2×C4⋊C4×D47C2214yes—
23C2×C4⋊C4×D47C2214yes—
24C2×C4⋊C4×D47C2212yes—
25C2×C42×D47C2211yescharacteristic
26C2×C42×D47C2214yes—
27C2×C42×D47C2211yescharacteristic
28C2×C42×D47C2211yescharacteristic
29#15689022C2214yes—
30#15689022C2212yes—
31#15689021C2214yes—
32#15689021C2212yes—
33#15689020C2214yes—
34#15689020C2214yes—
35#15689020C2214yes—
36#15689019C2212yes—
37#15689019C2214yes—
38#15689018C2214yes—
39#15689018C2214yes—
40#15689018C2214yes—
41#15689010C2214yes—
42#15689009C2214yes—
43#15689008C2214yes—
44#15689007C2214yes—
45#15689006C2214yes—
46#15689005C2214yes—
47#15689004C2214yes—
48#15688993C2211yescharacteristic
49#15688992C2214yes—
50#15688992C2212yes—
51C4⋊C4×Dic47C2212yes—
52C4⋊C4×Dic47C2212yes—
53C4×Dic47⋊C4C2214yes—
54C4×C4⋊Dic47C2212yes—
55#15688974C2214yes—
56#15688969C2211yescharacteristic
57#15688969C2211yescharacteristic
58#15688969C2211yescharacteristic
59#15688968C2212yes—
60#15688968C2212yes—
61#95×D47C2214yes—
62#95×D47C2212yes—
63#95×D47C2214yes—
64#95×D47C2212yes—
65C2×#125×C47C2211yescharacteristic
66C47×#389C2214yes—
67C47×#389C2212yes—
68C47×#387C2214yes—
69C47×#384C2211yescharacteristic
70C4×C4⋊C4×C47C2212yes—
71C47×#376C2211yescharacteristic
72C22×C4×D47C2311yescharacteristic
73C22×C4×D47C2311yescharacteristic
74C22×C4×D47C2314yes—
75C22×C4×D47C2314yes—
76C22×C4×D47C2312yes—
77C22×C4×D47C2312yes—
78C22×C4×D47C2311yescharacteristic
79#13094016C2×C418yescomplemented
80#13094015C2×C4116yescomplemented
81#13094014C2×C4132yescomplemented
82C2×C4⋊Dic47C2312yes—
83C2×C4⋊Dic47C2314yes—
84C2×C4⋊Dic47C2314yes—
85C2×C4⋊Dic47C2312yes—
86C2×C4⋊Dic47C2314yes—
87C2×Dic47⋊C4C2314yes—
88C2×Dic47⋊C4C2314yes—
89C2×Dic47⋊C4C2314yes—
90C2×Dic47⋊C4C2314yes—
91C2×Dic47⋊C4C2314yes—
92C2×Dic47⋊C4C2314yes—
93C2×Dic47⋊C4C2314yes—
94C2×Dic47⋊C4C2314yes—
95C4⋊C4×D47—28no—
96C4⋊C4×D47—48no—
97C4⋊C4×D47—48no—
98C4⋊C4×D47C2×C4116yes—
99C4⋊C4×D47C2×C4132yes—
100C2×C4×Dic47C2311yescharacteristic
101C2×C4×Dic47C2311yescharacteristic
102C2×C4×Dic47C2311yescharacteristic
103C2×C4×Dic47C2314yes—
104C2×C4×Dic47C2314yes—
105C2×C4×Dic47C2314yes—
106C2×C4×Dic47C2312yes—
107C2×C4×Dic47C2311yescharacteristic
108C2×C4×Dic47C2312yes—
109C2×C4×Dic47C2311yescharacteristic
110C42×D47—24no—
111C42×D47—48no—
112C42×D47C2×C418yes—
113C42×D47Q818yes—
114C47⋊#95C2312yes—
115C47⋊#95C2312yes—
116C47⋊#95C2312yes—
117C47⋊#95C2312yes—
118C47⋊#95C2312yes—
119C47⋊#95C2312yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126#125×C47C2×C418yescomplemented
127C2×C4⋊C4×C47C2312yes—
128C2×C4⋊C4×C47C2314yes—
129C2×C4⋊C4×C47C2314yes—
130C2×C4⋊C4×C47C2312yes—
131C2×C4⋊C4×C47C2314yes—
132C2×C42×C47C2311yescharacteristic
133C2×C42×C47C2314yes—
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136#95×C47C2312yes—
137#95×C47C2312yes—
138#95×C47C2314yes—
139#95×C47C2314yes—
140C23×D47C2411yescharacteristic
141C22×C4×C47C2411yescharacteristic
142C22×C4×C47C2414yes—
143C22×C4×C47C2411yescharacteristic
144C22×C4×C47C2414yes—
145C22×C4×C47C2412yes—
146C22×C4×C47C2412yes—
147C22×C4×C47C2411yescharacteristic
148C22×Dic47C2411yescharacteristic
149C22×Dic47C2411yescharacteristic
150C22×Dic47C2414yes—
151C22×Dic47C2414yes—
152C22×Dic47C2412yes—
153C22×Dic47C2412yes—
154C22×Dic47C2411yescharacteristic
155C2×C4×D47—24no—
156C2×C4×D47—28no—
157C2×C4×D47—24no—
158C2×C4×D47—28no—
159C2×C4×D47—24no—
160C2×C4×D47—24no—
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—28no—
164C2×C4×D47—28no—
165C2×C4×D47—24no—
166C2×C4×D47—28no—
167C2×C4×D47—24no—
168C2×C4×D47C22×C418yes—
169C2×C4×D47C22×C4116yes—
170C2×C4×D47C22×C414yes—
171C2×C4×D47C2×Q818yes—
172C2×C4×D47C2×Q814yes—
173C2×C4×D47#4114yes—
174C4⋊C4×C47—24no—
175C4⋊C4×C47—44no—
176C4⋊C4×C47—44no—
177C4⋊C4×C47C22×C4116yes—
178C4⋊C4×C47C22×C418yes—
179C42×C47—22no—
180C42×C47—44no—
181C42×C47C22×C414yes—
182C42×C47C2×Q814yes—
183C4⋊Dic47—24no—
184C4⋊Dic47—44no—
185C4⋊Dic47—44no—
186C4⋊Dic47C22×C4116yes—
187C4⋊Dic47C22×C418yes—
188Dic47⋊C4—28no—
189Dic47⋊C4—44no—
190Dic47⋊C4—44no—
191Dic47⋊C4—44no—
192Dic47⋊C4—44no—
193Dic47⋊C4C22×C4116yes—
194Dic47⋊C4C22×C4116yes—
195Dic47⋊C4C22×C4116yes—
196C4×Dic47—22no—
197C4×Dic47—22no—
198C4×Dic47—22no—
199C4×Dic47—44no—
200C4×Dic47—44no—
201C4×Dic47—44no—
202C4×Dic47C22×C418yes—
203C4×Dic47C22×C414yes—
204C4×Dic47C2×Q814yes—
205C4×Dic47C2×Q818yes—
206C23×C47C2511yescharacteristic
207C22×D47C23×C412yes—
208C22×D47C22×Q812yes—
209C22×D47C2×#4112yes—
210C22×D47H(5,𝔽2)14yes—
211C22×D472−1+414yes—
212C2×C4×C47—22no—
213C2×C4×C47—24no—
214C2×C4×C47—22no—
215C2×C4×C47—24no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—24no—
221C2×C4×C47—24no—
222C2×C4×C47—22no—
223C2×C4×C47—24no—
224C2×C4×C47—22no—
225C2×C4×C47C23×C414yes—
226C2×C4×C47C23×C418yes—
227C2×C4×C47C23×C412yes—
228C2×C4×C47C22×Q814yes—
229C2×C4×C47C22×Q812yes—
230C2×C4×C47C2×#4112yes—
231C2×Dic47—22no—
232C2×Dic47—24no—
233C2×Dic47—22no—
234C2×Dic47—24no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—21no—
238C2×Dic47—21no—
239C2×Dic47—24no—
240C2×Dic47—24no—
241C2×Dic47—22no—
242C2×Dic47—24no—
243C2×Dic47—22no—
244C2×Dic47C23×C414yes—
245C2×Dic47C23×C418yes—
246C2×Dic47C23×C412yes—
247C2×Dic47C22×Q814yes—
248C2×Dic47C22×Q812yes—
249C2×Dic47C2×#4112yes—
250C4×D47—232no—
251C4×D47—216no—
252C4×D47—216no—
253C4×D47—44no—
254C4×D47—416no—
255C4×D47—44no—
256C4×D47C4×Q8116yes—
257C2×#2330—471nomaximal, Sylow
258C22×C47C24×C411yescharacteristic
259C22×C47C23×Q811yescharacteristic
260C22×C47C22×#4111yescharacteristic
261C22×C47C2×H(5,𝔽2)12yes—
262C22×C47C2×2−1+412yes—
263C2×D47C2×C4×Q814yes—
264C2×D47#52018yes—
265C2×D47#54014yes—
266C2×D47#54114yes—
267C2×D47#54418yes—
268C4×C47—28no—
269C4×C47—24no—
270C4×C47—24no—
271C4×C47—41no—
272C4×C47—44no—
273C4×C47—41no—
274C4×C47C2×C4×Q814yes—
275Dic47—28no—
276Dic47—24no—
277Dic47—24no—
278Dic47—41no—
279Dic47—44no—
280Dic47—41no—
281Dic47C2×C4×Q814yes—
282C22×#125—471no—
283#2330—474no—
284#2330—472no—
285#2330—474no—
286#2330—471no—
287#2330—472no—
288#2330—471no—
289#2330—471no—
290#2330D4711yescharacteristic, direct product factor
291C2×#389—472no—
292C2×#389—474no—
293C2×#387—474no—
294C2×#384—471no—
295C2×C4×C4⋊C4—472no—
296C2×#376—471no—
297C2×C47C22×C4×Q811yescharacteristic
298C2×C47C2×#52012yes—
299C2×C47C2×#54011yescharacteristic
300C2×C47C2×#54111yescharacteristic
301C2×C47C2×#54412yes—
302D47#233018yesdirect product factor
303C2×#125—4716no—
304C2×#125—474no—
305C2×#125—472no—
306C2×#125—471no—
307C2×#125C2×D4711yescharacteristic
308C22×C4⋊C4—472no—
309C22×C4⋊C4—474no—
310C22×C4⋊C4—472no—
311C22×C4⋊C4—474no—
312C22×C4⋊C4—474no—
313C22×C42—471no—
314C22×C42—471no—
315C22×C42—471no—
316C22×C42—474no—
317#389—474no—
318#389—474no—
319#389—474no—
320#389—474no—
321#389—472no—
322#389—474no—
323#389—472no—
324#389—474no—
325#389—472no—
326#389—474no—
327#389—474no—
328#389—474no—
329#389C2×D4714yes—
330#389C2×D4712yes—
331#387—474no—
332#387—474no—
333#387—474no—
334#387—474no—
335#387—474no—
336#387—474no—
337#387—474no—
338#387C2×D4714yes—
339#384—474no—
340#384—472no—
341#384—471no—
342#384C2×D4711yescharacteristic
343C4×C4⋊C4—472no—
344C4×C4⋊C4—472no—
345C4×C4⋊C4—472no—
346C4×C4⋊C4—474no—
347C4×C4⋊C4—474no—
348C4×C4⋊C4C2×D4712yes—
349#376—471no—
350#376—471no—
351#376—471no—
352#376—472no—
353#376—472no—
354#376C2×D4711yescharacteristic
355C2×#95—472no—
356C2×#95—472no—
357C2×#95—474no—
358C2×#95—474no—
359C47C2×#233011yescharacteristic, complemented, Sylow
360C23×C4—471no—
361C23×C4—472no—
362C23×C4—474no—
363C23×C4—472no—
364C23×C4—471no—
365C23×C4—474no—
366C23×C4—471no—
367#125—4732no—
368#125—4716no—
369#125—478no—
370#125C4×D4718yescomplemented
371C2×C4⋊C4—474no—
372C2×C4⋊C4—474no—
373C2×C4⋊C4—474no—
374C2×C4⋊C4—472no—
375C2×C4⋊C4—474no—
376C2×C4⋊C4—4716no—
377C2×C4⋊C4—4732no—
378C2×C4⋊C4—474no—
379C2×C4⋊C4—472no—
380C2×C4⋊C4—474no—
381C2×C4⋊C4—474no—
382C2×C4⋊C4—474no—
383C2×C4⋊C4—474no—
384C2×C4⋊C4—474no—
385C2×C4⋊C4—474no—
386C2×C4⋊C4—948no—
387C2×C4⋊C4—1888no—
388C2×C4⋊C4—1888no—
389C2×C4⋊C4C22×D4712yes—
390C2×C4⋊C4C22×D4714yes—
391C2×C4⋊C4C22×D4714yes—
392C2×C4⋊C4C22×D4712yes—
393C2×C4⋊C4C22×D4714yes—
394C2×C42—472no—
395C2×C42—471no—
396C2×C42—472no—
397C2×C42—471no—
398C2×C42—478no—
399C2×C42—478no—
400C2×C42—471no—
401C2×C42—471no—
402C2×C42—471no—
403C2×C42—474no—
404C2×C42—474no—
405C2×C42—474no—
406C2×C42—944no—
407C2×C42—1888no—
408C2×C42C22×D4711yescharacteristic
409C2×C42C22×D4714yes—
410C2×C42C22×D4711yescharacteristic
411C2×C42C22×D4711yescharacteristic
412#95—472no—
413#95—472no—
414#95—472no—
415#95—472no—
416#95—472no—
417#95—472no—
418#95—474no—
419#95—474no—
420#95—474no—
421#95—474no—
422#95—474no—
423#95—474no—
424#95C22×D4712yes—
425#95C22×D4712yes—
426#95C22×D4714yes—
427#95C22×D4714yes—
428C24—471no—
429C22×C4—471no—
430C22×C4—474no—
431C22×C4—474no—
432C22×C4—474no—
433C22×C4—472no—
434C22×C4—472no—
435C22×C4—474no—
436C22×C4—478no—
437C22×C4—4716no—
438C22×C4—478no—
439C22×C4—471no—
440C22×C4—471no—
441C22×C4—474no—
442C22×C4—944no—
443C22×C4—948no—
444C22×C4—944no—
445C22×C4—944no—
446C22×C4—948no—
447C22×C4—944no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—948no—
451C22×C4—948no—
452C22×C4—944no—
453C22×C4—948no—
454C22×C4—944no—
455C22×C4C23×D4711yescharacteristic
456C22×C4C23×D4711yescharacteristic
457C22×C4C23×D4714yes—
458C22×C4C23×D4714yes—
459C22×C4C23×D4712yes—
460C22×C4C23×D4712yes—
461C22×C4C23×D4711yescharacteristic
462C4⋊C4—24no—
463C4⋊C4—44no—
464C4⋊C4—44no—
465C4⋊C4—4716no—
466C4⋊C4—4716no—
467C4⋊C4—4716no—
468C4⋊C4—4716no—
469C4⋊C4—478no—
470C4⋊C4—948no—
471C4⋊C4—944no—
472C4⋊C4—1884no—
473C4⋊C4—1884no—
474C4⋊C4—1884no—
475C4⋊C4—1884no—
476C4⋊C4—1884no—
477C4⋊C4—1884no—
478C4⋊C4C2×C4×D47116yes—
479C4⋊C4C2×C4×D4718yes—
480C42—22no—
481C42—44no—
482C42—478no—
483C42—474no—
484C42—478no—
485C42—474no—
486C42—942no—
487C42—942no—
488C42—942no—
489C42—1884no—
490C42—1884no—
491C42—1884no—
492C42C2×C4×D4714yes—
493C42Q8×D4714yes—
494C23—472no—
495C23—472no—
496C23—472no—
497C23—474no—
498C23—474no—
499C23C24×D4711yescharacteristic
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—472no—
514C2×C4—472no—
515C2×C4—472no—
516C2×C4—4716no—
517C2×C4—474no—
518C2×C4—478no—
519C2×C4—474no—
520C2×C4—9416no—
521C2×C4—9416no—
522C2×C4—9432no—
523C2×C4—942no—
524C2×C4—944no—
525C2×C4—942no—
526C2×C4—942no—
527C2×C4—942no—
528C2×C4—944no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—944no—
532C2×C4—944no—
533C2×C4—942no—
534C2×C4—944no—
535C2×C4—942no—
536C2×C4—1884no—
537C2×C4—18816no—
538C2×C4—1884no—
539C2×C4C22×C4×D4714yes—
540C2×C4C22×C4×D4718yes—
541C2×C4C22×C4×D4712yes—
542C2×C4C2×Q8×D4714yes—
543C2×C4C2×Q8×D4712yes—
544C2×C4#41×D4712yes—
545C22—478no—
546C22—474no—
547C22—478no—
548C22—474no—
549C22—474no—
550C22C23×C4×D4711yescharacteristic
551C22C22×Q8×D4711yescharacteristic
552C22C2×#41×D4711yescharacteristic
553C22H(5,𝔽2)×D4712yes—
554C222−1+4×D4712yes—
555C4—24no—
556C4—28no—
557C4—24no—
558C4—41no—
559C4—44no—
560C4—41no—
561C4—474no—
562C4—944no—
563C4—944no—
564C4—948no—
565C4—1881no—
566C4—1884no—
567C4—1881no—
568C4C4×Q8×D4714yes—
569C2—478no—
570C2C2×C4×Q8×D4711yescharacteristic
571C2#520×D4712yes—
572C2#540×D4711yescharacteristic
573C2#541×D4711yescharacteristic
574C2#544×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2330C2
socle, cosocleC23×C47C25
prime radicalC23×D47C24
hypercenter#2330D47
hypocenterC47C2×#2330
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2330

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20246130C2semidirect
3. #20246129C2semidirect
4. #20246128C2semidirect
5. #20246127C2semidirect
6. #20246126C2semidirect
7. #20246125C2semidirect
8. #20246124C2semidirect
15. C47×#2330C2semidirect
19. #125×D47C4semidirect
79. #13094016C2×C4semidirect
80. #13094015C2×C4semidirect
81. #13094014C2×C4semidirect
126. #125×C47C2×C4semidirect
290. #2330D47direct (N × H)
302. D47#2330direct (N × H)
359. C47C2×#2330semidirect
370. #125C4×D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#125×D472
#202461302
#202461292
#202461282
#202461272
#202461262
#202461252
#202461242
#389×D472
#387×D472
#384×D472
C4×C4⋊C4×D472
#376×D472
C47×#23302
C2×#233047